Two-Dimensional Approximations by the Method of Dividing Toric Tilings

Abstract

An infinite sequence of dividing two-dimensional toric tilings is constructed by the differentiation method. The karyons of the tilings have radii tending to zero and contain points having the best approximations on the torus in certain normalized metrics, which are defined by the initial karyon. The properties of the latter metrics can be essentially different from those of the standard metrics on a torus, used in approximation problems.